Integrand size = 141, antiderivative size = 28 \[ \int \frac {-10 e^x x^2+25 x^3-2 e^{2 x} x^3+\left (9325 x^2-750 e^{2 x} x^2+e^x \left (-1250 x-10 x^3\right )\right ) \log (x)+\left (1171875 x-93750 e^{2 x} x+e^x \left (-1250 x-2500 x^2\right )\right ) \log ^2(x)+\left (48828125-3906250 e^{2 x}+e^x (-156250-156250 x)-6250 x\right ) \log ^3(x)}{25 x^3+9375 x^2 \log (x)+1171875 x \log ^2(x)+48828125 \log ^3(x)} \, dx=-1+x-\frac {1}{25} \left (e^x+\frac {x}{25+\frac {x}{5 \log (x)}}\right )^2 \] Output:
x-1/5*(x/(25+1/5*x/ln(x))+exp(x))*(1/5*x/(25+1/5*x/ln(x))+1/5*exp(x))-1
Leaf count is larger than twice the leaf count of optimal. \(59\) vs. \(2(28)=56\).
Time = 0.10 (sec) , antiderivative size = 59, normalized size of antiderivative = 2.11 \[ \int \frac {-10 e^x x^2+25 x^3-2 e^{2 x} x^3+\left (9325 x^2-750 e^{2 x} x^2+e^x \left (-1250 x-10 x^3\right )\right ) \log (x)+\left (1171875 x-93750 e^{2 x} x+e^x \left (-1250 x-2500 x^2\right )\right ) \log ^2(x)+\left (48828125-3906250 e^{2 x}+e^x (-156250-156250 x)-6250 x\right ) \log ^3(x)}{25 x^3+9375 x^2 \log (x)+1171875 x \log ^2(x)+48828125 \log ^3(x)} \, dx=\frac {-625 e^{2 x}+15625 x-50 e^x x-x^2-\frac {x^4}{(x+125 \log (x))^2}+\frac {2 x^2 \left (25 e^x+x\right )}{x+125 \log (x)}}{15625} \] Input:
Integrate[(-10*E^x*x^2 + 25*x^3 - 2*E^(2*x)*x^3 + (9325*x^2 - 750*E^(2*x)* x^2 + E^x*(-1250*x - 10*x^3))*Log[x] + (1171875*x - 93750*E^(2*x)*x + E^x* (-1250*x - 2500*x^2))*Log[x]^2 + (48828125 - 3906250*E^(2*x) + E^x*(-15625 0 - 156250*x) - 6250*x)*Log[x]^3)/(25*x^3 + 9375*x^2*Log[x] + 1171875*x*Lo g[x]^2 + 48828125*Log[x]^3),x]
Output:
(-625*E^(2*x) + 15625*x - 50*E^x*x - x^2 - x^4/(x + 125*Log[x])^2 + (2*x^2 *(25*E^x + x))/(x + 125*Log[x]))/15625
Below are the steps used by Rubi to obtain the solution. The rule number used for the transformation is given above next to the arrow. The rules definitions used are listed below.
| \(\displaystyle \int \frac {-2 e^{2 x} x^3+25 x^3-10 e^x x^2+\left (e^x \left (-2500 x^2-1250 x\right )-93750 e^{2 x} x+1171875 x\right ) \log ^2(x)+\left (e^x \left (-10 x^3-1250 x\right )-750 e^{2 x} x^2+9325 x^2\right ) \log (x)+\left (e^x (-156250 x-156250)-3906250 e^{2 x}-6250 x+48828125\right ) \log ^3(x)}{25 x^3+9375 x^2 \log (x)+48828125 \log ^3(x)+1171875 x \log ^2(x)} \, dx\) |
| \(\Big \downarrow \) 7292 |
| \(\displaystyle \int \frac {-2 e^{2 x} x^3+25 x^3-10 e^x x^2+\left (e^x \left (-2500 x^2-1250 x\right )-93750 e^{2 x} x+1171875 x\right ) \log ^2(x)+\left (e^x \left (-10 x^3-1250 x\right )-750 e^{2 x} x^2+9325 x^2\right ) \log (x)+\left (e^x (-156250 x-156250)-3906250 e^{2 x}-6250 x+48828125\right ) \log ^3(x)}{25 (x+125 \log (x))^3}dx\) |
| \(\Big \downarrow \) 27 |
| \(\displaystyle \frac {1}{25} \int -\frac {2 e^{2 x} x^3-25 x^3+10 e^x x^2-3125 \left (-2 x-1250 e^{2 x}-50 e^x (x+1)+15625\right ) \log ^3(x)-625 \left (-150 e^{2 x} x+1875 x-2 e^x \left (2 x^2+x\right )\right ) \log ^2(x)-5 \left (-150 e^{2 x} x^2+1865 x^2-2 e^x \left (x^3+125 x\right )\right ) \log (x)}{(x+125 \log (x))^3}dx\) |
| \(\Big \downarrow \) 25 |
| \(\displaystyle -\frac {1}{25} \int \frac {2 e^{2 x} x^3-25 x^3+10 e^x x^2-3125 \left (-2 x-1250 e^{2 x}-50 e^x (x+1)+15625\right ) \log ^3(x)-625 \left (-150 e^{2 x} x+1875 x-2 e^x \left (2 x^2+x\right )\right ) \log ^2(x)-5 \left (-150 e^{2 x} x^2+1865 x^2-2 e^x \left (x^3+125 x\right )\right ) \log (x)}{(x+125 \log (x))^3}dx\) |
| \(\Big \downarrow \) 7293 |
| \(\displaystyle -\frac {1}{25} \int \left (-\frac {25 x^3}{(x+125 \log (x))^3}-\frac {9325 \log (x) x^2}{(x+125 \log (x))^3}+\frac {6250 \log ^3(x) x}{(x+125 \log (x))^3}-\frac {1171875 \log ^2(x) x}{(x+125 \log (x))^3}+2 e^{2 x}+\frac {10 e^x \left (\log (x) x^2+125 \log ^2(x) x+x+125 \log ^2(x)\right )}{(x+125 \log (x))^2}-\frac {48828125 \log ^3(x)}{(x+125 \log (x))^3}\right )dx\) |
| \(\Big \downarrow \) 2009 |
| \(\displaystyle \frac {1}{25} \left (\frac {2}{625} \int \frac {x^4}{(x+125 \log (x))^3}dx+\frac {2}{5} \int \frac {x^3}{(x+125 \log (x))^3}dx-\frac {6}{625} \int \frac {x^3}{(x+125 \log (x))^2}dx-\frac {2}{5} \int \frac {x^2}{(x+125 \log (x))^2}dx+\frac {6}{625} \int \frac {x^2}{x+125 \log (x)}dx-\frac {x^2}{625}-\frac {10 e^x \left (x^2 \log (x)+125 x \log ^2(x)\right )}{(x+125 \log (x))^2}+25 x-e^{2 x}\right )\) |
Input:
Int[(-10*E^x*x^2 + 25*x^3 - 2*E^(2*x)*x^3 + (9325*x^2 - 750*E^(2*x)*x^2 + E^x*(-1250*x - 10*x^3))*Log[x] + (1171875*x - 93750*E^(2*x)*x + E^x*(-1250 *x - 2500*x^2))*Log[x]^2 + (48828125 - 3906250*E^(2*x) + E^x*(-156250 - 15 6250*x) - 6250*x)*Log[x]^3)/(25*x^3 + 9375*x^2*Log[x] + 1171875*x*Log[x]^2 + 48828125*Log[x]^3),x]
Output:
$Aborted
Time = 0.15 (sec) , antiderivative size = 52, normalized size of antiderivative = 1.86
\[-\frac {x^{2}}{15625}+x -\frac {{\mathrm e}^{2 x}}{25}-\frac {2 \,{\mathrm e}^{x} x}{625}+\frac {\left (x^{2}+50 \,{\mathrm e}^{x} x +250 x \ln \left (x \right )+6250 \,{\mathrm e}^{x} \ln \left (x \right )\right ) x^{2}}{15625 \left (125 \ln \left (x \right )+x \right )^{2}}\]
Input:
int(((-3906250*exp(x)^2+(-156250*x-156250)*exp(x)-6250*x+48828125)*ln(x)^3 +(-93750*x*exp(x)^2+(-2500*x^2-1250*x)*exp(x)+1171875*x)*ln(x)^2+(-750*exp (x)^2*x^2+(-10*x^3-1250*x)*exp(x)+9325*x^2)*ln(x)-2*exp(x)^2*x^3-10*exp(x) *x^2+25*x^3)/(48828125*ln(x)^3+1171875*x*ln(x)^2+9375*x^2*ln(x)+25*x^3),x)
Output:
-1/15625*x^2+x-1/25*exp(2*x)-2/625*exp(x)*x+1/15625*(x^2+50*exp(x)*x+250*x *ln(x)+6250*exp(x)*ln(x))*x^2/(125*ln(x)+x)^2
Leaf count of result is larger than twice the leaf count of optimal. 81 vs. \(2 (23) = 46\).
Time = 0.11 (sec) , antiderivative size = 81, normalized size of antiderivative = 2.89 \[ \int \frac {-10 e^x x^2+25 x^3-2 e^{2 x} x^3+\left (9325 x^2-750 e^{2 x} x^2+e^x \left (-1250 x-10 x^3\right )\right ) \log (x)+\left (1171875 x-93750 e^{2 x} x+e^x \left (-1250 x-2500 x^2\right )\right ) \log ^2(x)+\left (48828125-3906250 e^{2 x}+e^x (-156250-156250 x)-6250 x\right ) \log ^3(x)}{25 x^3+9375 x^2 \log (x)+1171875 x \log ^2(x)+48828125 \log ^3(x)} \, dx=\frac {25 \, x^{3} - x^{2} e^{\left (2 \, x\right )} - 25 \, {\left (x^{2} + 50 \, x e^{x} - 15625 \, x + 625 \, e^{\left (2 \, x\right )}\right )} \log \left (x\right )^{2} - 10 \, {\left (x^{2} e^{x} - 625 \, x^{2} + 25 \, x e^{\left (2 \, x\right )}\right )} \log \left (x\right )}{25 \, {\left (x^{2} + 250 \, x \log \left (x\right ) + 15625 \, \log \left (x\right )^{2}\right )}} \] Input:
integrate(((-3906250*exp(x)^2+(-156250*x-156250)*exp(x)-6250*x+48828125)*l og(x)^3+(-93750*x*exp(x)^2+(-2500*x^2-1250*x)*exp(x)+1171875*x)*log(x)^2+( -750*exp(x)^2*x^2+(-10*x^3-1250*x)*exp(x)+9325*x^2)*log(x)-2*exp(x)^2*x^3- 10*exp(x)*x^2+25*x^3)/(48828125*log(x)^3+1171875*x*log(x)^2+9375*x^2*log(x )+25*x^3),x, algorithm="fricas")
Output:
1/25*(25*x^3 - x^2*e^(2*x) - 25*(x^2 + 50*x*e^x - 15625*x + 625*e^(2*x))*l og(x)^2 - 10*(x^2*e^x - 625*x^2 + 25*x*e^(2*x))*log(x))/(x^2 + 250*x*log(x ) + 15625*log(x)^2)
Leaf count of result is larger than twice the leaf count of optimal. 70 vs. \(2 (17) = 34\).
Time = 0.16 (sec) , antiderivative size = 70, normalized size of antiderivative = 2.50 \[ \int \frac {-10 e^x x^2+25 x^3-2 e^{2 x} x^3+\left (9325 x^2-750 e^{2 x} x^2+e^x \left (-1250 x-10 x^3\right )\right ) \log (x)+\left (1171875 x-93750 e^{2 x} x+e^x \left (-1250 x-2500 x^2\right )\right ) \log ^2(x)+\left (48828125-3906250 e^{2 x}+e^x (-156250-156250 x)-6250 x\right ) \log ^3(x)}{25 x^3+9375 x^2 \log (x)+1171875 x \log ^2(x)+48828125 \log ^3(x)} \, dx=- \frac {x^{2}}{15625} + x + \frac {x^{4} + 250 x^{3} \log {\left (x \right )}}{15625 x^{2} + 3906250 x \log {\left (x \right )} + 244140625 \log {\left (x \right )}^{2}} + \frac {- 50 x e^{x} \log {\left (x \right )} + \left (- 5 x - 625 \log {\left (x \right )}\right ) e^{2 x}}{125 x + 15625 \log {\left (x \right )}} \] Input:
integrate(((-3906250*exp(x)**2+(-156250*x-156250)*exp(x)-6250*x+48828125)* ln(x)**3+(-93750*x*exp(x)**2+(-2500*x**2-1250*x)*exp(x)+1171875*x)*ln(x)** 2+(-750*exp(x)**2*x**2+(-10*x**3-1250*x)*exp(x)+9325*x**2)*ln(x)-2*exp(x)* *2*x**3-10*exp(x)*x**2+25*x**3)/(48828125*ln(x)**3+1171875*x*ln(x)**2+9375 *x**2*ln(x)+25*x**3),x)
Output:
-x**2/15625 + x + (x**4 + 250*x**3*log(x))/(15625*x**2 + 3906250*x*log(x) + 244140625*log(x)**2) + (-50*x*exp(x)*log(x) + (-5*x - 625*log(x))*exp(2* x))/(125*x + 15625*log(x))
Leaf count of result is larger than twice the leaf count of optimal. 84 vs. \(2 (23) = 46\).
Time = 0.07 (sec) , antiderivative size = 84, normalized size of antiderivative = 3.00 \[ \int \frac {-10 e^x x^2+25 x^3-2 e^{2 x} x^3+\left (9325 x^2-750 e^{2 x} x^2+e^x \left (-1250 x-10 x^3\right )\right ) \log (x)+\left (1171875 x-93750 e^{2 x} x+e^x \left (-1250 x-2500 x^2\right )\right ) \log ^2(x)+\left (48828125-3906250 e^{2 x}+e^x (-156250-156250 x)-6250 x\right ) \log ^3(x)}{25 x^3+9375 x^2 \log (x)+1171875 x \log ^2(x)+48828125 \log ^3(x)} \, dx=\frac {25 \, x^{3} + 6250 \, x^{2} \log \left (x\right ) - 25 \, {\left (x^{2} - 15625 \, x\right )} \log \left (x\right )^{2} - {\left (x^{2} + 250 \, x \log \left (x\right ) + 15625 \, \log \left (x\right )^{2}\right )} e^{\left (2 \, x\right )} - 10 \, {\left (x^{2} \log \left (x\right ) + 125 \, x \log \left (x\right )^{2}\right )} e^{x}}{25 \, {\left (x^{2} + 250 \, x \log \left (x\right ) + 15625 \, \log \left (x\right )^{2}\right )}} \] Input:
integrate(((-3906250*exp(x)^2+(-156250*x-156250)*exp(x)-6250*x+48828125)*l og(x)^3+(-93750*x*exp(x)^2+(-2500*x^2-1250*x)*exp(x)+1171875*x)*log(x)^2+( -750*exp(x)^2*x^2+(-10*x^3-1250*x)*exp(x)+9325*x^2)*log(x)-2*exp(x)^2*x^3- 10*exp(x)*x^2+25*x^3)/(48828125*log(x)^3+1171875*x*log(x)^2+9375*x^2*log(x )+25*x^3),x, algorithm="maxima")
Output:
1/25*(25*x^3 + 6250*x^2*log(x) - 25*(x^2 - 15625*x)*log(x)^2 - (x^2 + 250* x*log(x) + 15625*log(x)^2)*e^(2*x) - 10*(x^2*log(x) + 125*x*log(x)^2)*e^x) /(x^2 + 250*x*log(x) + 15625*log(x)^2)
Leaf count of result is larger than twice the leaf count of optimal. 93 vs. \(2 (23) = 46\).
Time = 0.14 (sec) , antiderivative size = 93, normalized size of antiderivative = 3.32 \[ \int \frac {-10 e^x x^2+25 x^3-2 e^{2 x} x^3+\left (9325 x^2-750 e^{2 x} x^2+e^x \left (-1250 x-10 x^3\right )\right ) \log (x)+\left (1171875 x-93750 e^{2 x} x+e^x \left (-1250 x-2500 x^2\right )\right ) \log ^2(x)+\left (48828125-3906250 e^{2 x}+e^x (-156250-156250 x)-6250 x\right ) \log ^3(x)}{25 x^3+9375 x^2 \log (x)+1171875 x \log ^2(x)+48828125 \log ^3(x)} \, dx=-\frac {10 \, x^{2} e^{x} \log \left (x\right ) + 25 \, x^{2} \log \left (x\right )^{2} + 1250 \, x e^{x} \log \left (x\right )^{2} - 25 \, x^{3} + x^{2} e^{\left (2 \, x\right )} - 6250 \, x^{2} \log \left (x\right ) + 250 \, x e^{\left (2 \, x\right )} \log \left (x\right ) - 390625 \, x \log \left (x\right )^{2} + 15625 \, e^{\left (2 \, x\right )} \log \left (x\right )^{2}}{25 \, {\left (x^{2} + 250 \, x \log \left (x\right ) + 15625 \, \log \left (x\right )^{2}\right )}} \] Input:
integrate(((-3906250*exp(x)^2+(-156250*x-156250)*exp(x)-6250*x+48828125)*l og(x)^3+(-93750*x*exp(x)^2+(-2500*x^2-1250*x)*exp(x)+1171875*x)*log(x)^2+( -750*exp(x)^2*x^2+(-10*x^3-1250*x)*exp(x)+9325*x^2)*log(x)-2*exp(x)^2*x^3- 10*exp(x)*x^2+25*x^3)/(48828125*log(x)^3+1171875*x*log(x)^2+9375*x^2*log(x )+25*x^3),x, algorithm="giac")
Output:
-1/25*(10*x^2*e^x*log(x) + 25*x^2*log(x)^2 + 1250*x*e^x*log(x)^2 - 25*x^3 + x^2*e^(2*x) - 6250*x^2*log(x) + 250*x*e^(2*x)*log(x) - 390625*x*log(x)^2 + 15625*e^(2*x)*log(x)^2)/(x^2 + 250*x*log(x) + 15625*log(x)^2)
Time = 4.10 (sec) , antiderivative size = 547, normalized size of antiderivative = 19.54 \[ \int \frac {-10 e^x x^2+25 x^3-2 e^{2 x} x^3+\left (9325 x^2-750 e^{2 x} x^2+e^x \left (-1250 x-10 x^3\right )\right ) \log (x)+\left (1171875 x-93750 e^{2 x} x+e^x \left (-1250 x-2500 x^2\right )\right ) \log ^2(x)+\left (48828125-3906250 e^{2 x}+e^x (-156250-156250 x)-6250 x\right ) \log ^3(x)}{25 x^3+9375 x^2 \log (x)+1171875 x \log ^2(x)+48828125 \log ^3(x)} \, dx=\frac {24\,x}{25}-\frac {{\mathrm {e}}^{2\,x}}{25}+9\,\ln \left (x\right )+\ln \left (x\right )\,\left ({\mathrm {e}}^x\,\left (\frac {\frac {x^5}{5}+\frac {129\,x^4}{5}+\frac {627\,x^3}{5}+1534525\,x^2+335175000\,x+17969531250}{x^3+375\,x^2+46875\,x+1953125}-\frac {1534425\,x^2+335175000\,x+17969531250}{x^3+375\,x^2+46875\,x+1953125}\right )+\frac {\frac {24\,x^4}{125}+72\,x^3+9000\,x^2+375000\,x}{x^3+375\,x^2+46875\,x+1953125}-\frac {\frac {18\,x^4}{125}+72\,x^3+12375\,x^2+796875\,x+17578125}{x^3+375\,x^2+46875\,x+1953125}\right )-\frac {62500\,x+5859375}{x^3+375\,x^2+46875\,x+1953125}-\frac {\frac {x\,\left (25\,x^3\,{\mathrm {e}}^x-3125\,x^2\,{\mathrm {e}}^x+25\,x^4\,{\mathrm {e}}^x+x^4\right )}{15625\,\left (x+125\right )}+\frac {x\,\ln \left (x\right )\,\left (75\,x^2\,{\mathrm {e}}^x+50\,x^3\,{\mathrm {e}}^x-3125\,x\,{\mathrm {e}}^x-125\,x^2+3\,x^3\right )}{125\,\left (x+125\right )}+\frac {x\,{\ln \left (x\right )}^2\,\left (25\,x^2\,{\mathrm {e}}^x+50\,x\,{\mathrm {e}}^x+3\,x^2\right )}{x+125}}{x^2+250\,x\,\ln \left (x\right )+15625\,{\ln \left (x\right )}^2}-\frac {\frac {x\,\left (406250\,x^3\,{\mathrm {e}}^x-390625\,x^2\,{\mathrm {e}}^x+21950\,x^4\,{\mathrm {e}}^x+3250\,x^5\,{\mathrm {e}}^x+25\,x^6\,{\mathrm {e}}^x-48828125\,x\,{\mathrm {e}}^x-1953125\,x^2+31250\,x^3+1000\,x^4+4\,x^5\right )}{15625\,{\left (x+125\right )}^3}+\frac {x\,{\ln \left (x\right )}^2\,\left (15675\,x^2\,{\mathrm {e}}^x+3225\,x^3\,{\mathrm {e}}^x+25\,x^4\,{\mathrm {e}}^x+12500\,x\,{\mathrm {e}}^x+1125\,x^2+6\,x^3\right )}{{\left (x+125\right )}^3}+\frac {x\,\ln \left (x\right )\,\left (428125\,x^2\,{\mathrm {e}}^x+37650\,x^3\,{\mathrm {e}}^x+6475\,x^4\,{\mathrm {e}}^x+50\,x^5\,{\mathrm {e}}^x+781250\,x\,{\mathrm {e}}^x+46875\,x^2+2000\,x^3+9\,x^4\right )}{125\,{\left (x+125\right )}^3}}{x+125\,\ln \left (x\right )}+\frac {x^2}{3125}+\frac {{\mathrm {e}}^x\,\left (\frac {x^6}{625}+\frac {131\,x^5}{625}+\frac {1129\,x^4}{625}+\frac {256\,x^3}{5}-50\,x^2-6250\,x\right )}{x^3+375\,x^2+46875\,x+1953125} \] Input:
int(-(10*x^2*exp(x) + 2*x^3*exp(2*x) + log(x)^2*(93750*x*exp(2*x) - 117187 5*x + exp(x)*(1250*x + 2500*x^2)) - 25*x^3 + log(x)^3*(6250*x + 3906250*ex p(2*x) + exp(x)*(156250*x + 156250) - 48828125) + log(x)*(750*x^2*exp(2*x) + exp(x)*(1250*x + 10*x^3) - 9325*x^2))/(1171875*x*log(x)^2 + 9375*x^2*lo g(x) + 48828125*log(x)^3 + 25*x^3),x)
Output:
(24*x)/25 - exp(2*x)/25 + 9*log(x) + log(x)*(exp(x)*((335175000*x + 153452 5*x^2 + (627*x^3)/5 + (129*x^4)/5 + x^5/5 + 17969531250)/(46875*x + 375*x^ 2 + x^3 + 1953125) - (335175000*x + 1534425*x^2 + 17969531250)/(46875*x + 375*x^2 + x^3 + 1953125)) + (375000*x + 9000*x^2 + 72*x^3 + (24*x^4)/125)/ (46875*x + 375*x^2 + x^3 + 1953125) - (796875*x + 12375*x^2 + 72*x^3 + (18 *x^4)/125 + 17578125)/(46875*x + 375*x^2 + x^3 + 1953125)) - (62500*x + 58 59375)/(46875*x + 375*x^2 + x^3 + 1953125) - ((x*(25*x^3*exp(x) - 3125*x^2 *exp(x) + 25*x^4*exp(x) + x^4))/(15625*(x + 125)) + (x*log(x)*(75*x^2*exp( x) + 50*x^3*exp(x) - 3125*x*exp(x) - 125*x^2 + 3*x^3))/(125*(x + 125)) + ( x*log(x)^2*(25*x^2*exp(x) + 50*x*exp(x) + 3*x^2))/(x + 125))/(15625*log(x) ^2 + 250*x*log(x) + x^2) - ((x*(406250*x^3*exp(x) - 390625*x^2*exp(x) + 21 950*x^4*exp(x) + 3250*x^5*exp(x) + 25*x^6*exp(x) - 48828125*x*exp(x) - 195 3125*x^2 + 31250*x^3 + 1000*x^4 + 4*x^5))/(15625*(x + 125)^3) + (x*log(x)^ 2*(15675*x^2*exp(x) + 3225*x^3*exp(x) + 25*x^4*exp(x) + 12500*x*exp(x) + 1 125*x^2 + 6*x^3))/(x + 125)^3 + (x*log(x)*(428125*x^2*exp(x) + 37650*x^3*e xp(x) + 6475*x^4*exp(x) + 50*x^5*exp(x) + 781250*x*exp(x) + 46875*x^2 + 20 00*x^3 + 9*x^4))/(125*(x + 125)^3))/(x + 125*log(x)) + x^2/3125 + (exp(x)* ((256*x^3)/5 - 50*x^2 - 6250*x + (1129*x^4)/625 + (131*x^5)/625 + x^6/625) )/(46875*x + 375*x^2 + x^3 + 1953125)
Time = 0.16 (sec) , antiderivative size = 100, normalized size of antiderivative = 3.57 \[ \int \frac {-10 e^x x^2+25 x^3-2 e^{2 x} x^3+\left (9325 x^2-750 e^{2 x} x^2+e^x \left (-1250 x-10 x^3\right )\right ) \log (x)+\left (1171875 x-93750 e^{2 x} x+e^x \left (-1250 x-2500 x^2\right )\right ) \log ^2(x)+\left (48828125-3906250 e^{2 x}+e^x (-156250-156250 x)-6250 x\right ) \log ^3(x)}{25 x^3+9375 x^2 \log (x)+1171875 x \log ^2(x)+48828125 \log ^3(x)} \, dx=\frac {-15625 e^{2 x} \mathrm {log}\left (x \right )^{2}-250 e^{2 x} \mathrm {log}\left (x \right ) x -e^{2 x} x^{2}-1250 e^{x} \mathrm {log}\left (x \right )^{2} x -10 e^{x} \mathrm {log}\left (x \right ) x^{2}-25 \mathrm {log}\left (x \right )^{2} x^{2}+390625 \mathrm {log}\left (x \right )^{2} x +6250 \,\mathrm {log}\left (x \right ) x^{2}+25 x^{3}}{390625 \mathrm {log}\left (x \right )^{2}+6250 \,\mathrm {log}\left (x \right ) x +25 x^{2}} \] Input:
int(((-3906250*exp(x)^2+(-156250*x-156250)*exp(x)-6250*x+48828125)*log(x)^ 3+(-93750*x*exp(x)^2+(-2500*x^2-1250*x)*exp(x)+1171875*x)*log(x)^2+(-750*e xp(x)^2*x^2+(-10*x^3-1250*x)*exp(x)+9325*x^2)*log(x)-2*exp(x)^2*x^3-10*exp (x)*x^2+25*x^3)/(48828125*log(x)^3+1171875*x*log(x)^2+9375*x^2*log(x)+25*x ^3),x)
Output:
( - 15625*e**(2*x)*log(x)**2 - 250*e**(2*x)*log(x)*x - e**(2*x)*x**2 - 125 0*e**x*log(x)**2*x - 10*e**x*log(x)*x**2 - 25*log(x)**2*x**2 + 390625*log( x)**2*x + 6250*log(x)*x**2 + 25*x**3)/(25*(15625*log(x)**2 + 250*log(x)*x + x**2))